A difficult time dealt with by the Beatles (4,3)

I believe the answer is:

hard day

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'a difficult time dealt with by the beatles' is the definition.
I don't know anything about this answer so I cannot tell whether this works.

'difficult time dealt with by the beatles' is the wordplay.
I cannot quite understand how this works, but
'difficult' could be 'hard' (associated in meaning) and 'hard' is found in the answer.
'time' could be 'day' (day is a kind of time) and 'day' is found within the answer.
No letters remain.
This explanation may well be incorrect...

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